Multiply the following complex numbers, marked as blue dots on the graph: $(6) \cdot ( e^{17\pi i / 12})$ (Your current answer will be plotted in orange.)
Answer: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $6$ ) has angle $0$ and radius $6$ The second number ( $ e^{17\pi i / 12}$ ) has angle $\frac{17}{12}\pi$ and radius $1$ The radius of the result will be $6 \cdot 1$ , which is $6$ The angle of the result is $0 + \frac{17}{12}\pi = \frac{17}{12}\pi$ The radius of the result is $6$ and the angle of the result is $\frac{17}{12}\pi$.